Algebra Examples

$\frac{5}{7 - x} + \frac{3}{x - 7}$

Step 1

Factor $- 1$ out of $x$ .

$\frac{5}{7 - x} + \frac{3}{- 1 (- x) - 7}$

Step 2

Rewrite $- 7$ as $- 1 (7)$ .

$\frac{5}{7 - x} + \frac{3}{- 1 (- x) - 1 (7)}$

Step 3

Factor $- 1$ out of $- 1 (- x) - 1 (7)$ .

$\frac{5}{7 - x} + \frac{3}{- 1 (- x + 7)}$

Step 4

Simplify the expression.

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Step 4.1

Move a negative from the denominator of $\frac{3}{- 1 (- x + 7)}$ to the numerator.

$\frac{5}{7 - x} + \frac{- 1 \cdot 3}{- x + 7}$

Step 4.2

Reorder terms.

$\frac{5}{- x + 7} + \frac{- 1 \cdot 3}{- x + 7}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 - 1 \cdot 3}{- x + 7}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 1$ by $3$ .

$\frac{5 - 3}{- x + 7}$

Step 6.2

Subtract $3$ from $5$ .

$\frac{2}{- x + 7}$

Step 7

Factor $- 1$ out of $- x$ .

$\frac{2}{- (x) + 7}$

Step 8

Rewrite $7$ as $- 1 (- 7)$ .

$\frac{2}{- (x) - 1 (- 7)}$

Step 9

Factor $- 1$ out of $- (x) - 1 (- 7)$ .

$\frac{2}{- (x - 7)}$

Step 10

Rewrite negatives.

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Step 10.1

Rewrite $- (x - 7)$ as $- 1 (x - 7)$ .

$\frac{2}{- 1 (x - 7)}$

Step 10.2

Move the negative in front of the fraction.

$- \frac{2}{x - 7}$